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Pythagorean Theorem Area Demo

Pythagorean Theorem Area Demo
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2018-06-06 09:19
TriangleCircleCoordinate GeometryOptimizationGeometric Construction
This example demonstrates the Pythagorean theorem, focusing on the relationship between the sides of a right triangle and its area calculation. Core math concepts include the Pythagorean theorem, area computation, and coordinate geometry. It uses commands like Segment, Semicircle, Point, Polygon, Midpoint, Intersect, Vector, Translate, Line, Angle, OrthogonalLine, Circle for geometric construction and analysis, making it suitable for high school mathematics education and learning geometric constructions and optimization problems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Semicircle(A, B) → c
  3. Point(c) → C
  4. Polygon(A, C, B) → รูปหลายเหลี่ยม1, b, a, c_1
  5. Polygon(B, A, 4) → รูปหลายเหลี่ยม2, g, h, i, j, D, E
  6. Polygon(C, B, 4) → รูปหลายเหลี่ยม3, k, l, m, n, F, G
  7. Polygon(A, C, 4) → รูปหลายเหลี่ยม4, p, q, r, s, H, I
  8. Midpoint(A, B) → J
  9. Midpoint(A, D) → K
  10. Midpoint(D, E) → L
  11. Midpoint(B, E) → M
  12. Segment(J, L) → t
  13. Segment(K, M) → d
  14. Intersect(t, d) → N
  15. Midpoint(H, A) → O
  16. Segment(O, N) → e
  17. Point(e) → P
  18. Vector(O, P) → u
  19. Translate(รูปหลายเหลี่ยม4, u) → รูปหลายเหลี่ยม4'
  20. Line(L, l) → f_1
  21. Line(M, a) → g_1
  22. Line(J, n) → h_1
  23. Line(K, a) → i_1
  24. Intersect(g_1, h_1) → Q
  25. Intersect(h_1, i_1) → R
  26. Intersect(f_1, i_1) → S
  27. Polygon(J, A, K, R) → รูปหลายเหลี่ยม5, j_1, a_1, k_1, r_1
  28. Segment(R, B) → l_1
  29. Point(l_1) → T
  30. Vector(R, T) → v
  31. Translate(J, v) → J'
  32. Translate(A, v) → A'
  33. Translate(K, v) → K'
  34. Translate(R, v) → R'
  35. Polygon(J', A', K', R') → รูปหลายเหลี่ยม5', j', a', k', r'
  36. Polygon(J, Q, M, B) → รูปหลายเหลี่ยม6, j_2, q_1, m_1, b_1
  37. Segment(Q, C) → n_1
  38. Point(n_1) → U
  39. Vector(Q, U) → w
  40. Translate(J, w) → J'_1
  41. Translate(Q, w) → Q'
  42. Translate(M, w) → M'
  43. Translate(B, w) → B'
  44. Polygon(J'_1, Q', M', B') → รูปหลายเหลี่ยม6', j'_1, q', m', b'
  45. Polygon(D, L, S, K) → รูปหลายเหลี่ยม7, d_1, l_2, s_1, k_2
  46. Segment(S, F) → p_1
  47. Point(p_1) → V
  48. Vector(S, V) → u_1
  49. Translate(D, u_1) → D'
  50. Translate(L, u_1) → L'
  51. Translate(S, u_1) → S'
  52. Translate(K, u_1) → K'_1
  53. Polygon(D', L', S', K'_1) → รูปหลายเหลี่ยม7', d', l', s', k'_1
  54. Intersect(f_1, g_1) → W
  55. Polygon(W, L, E, M) → รูปหลายเหลี่ยม8, w_1, l_3, e_1, m_2
  56. Segment(W, G) → t_1
  57. Point(t_1) → Z
  58. Vector(W, Z) → v_1
  59. Translate(W, v_1) → W'
  60. Translate(L, v_1) → L'_1
  61. Translate(E, v_1) → E'
  62. Translate(M, v_1) → M'_1
  63. Polygon(W', L'_1, E', M'_1) → รูปหลายเหลี่ยม8', w', l'_1, e', m'_1
  64. Angle(A, C, B) → α
  65. Angle(A, I, H) → β
  66. Angle(I, H, C) → γ
  67. Angle(H, C, A) → δ
  68. Angle(C, A, I) → ε
  69. Angle(C, G, F) → ζ
  70. Angle(G, F, B) → η
  71. Angle(F, B, C) → θ
  72. Angle(B, C, G) → ι
  73. Angle(D, A, B) → κ
  74. Angle(A, B, E) → λ
  75. Angle(B, E, D) → μ
  76. Angle(E, D, A) → ν
  77. Intersect(m, n) → A_1
  78. Intersect(l, m) → B_1
  79. Intersect(q, r) → C_1
  80. Intersect(r, s) → D_1
  81. Line(E_1, A) → f_2
  82. Line(F_1, B) → g_2
  83. OrthogonalLine(C, g_2) → h_2
  84. Intersect(f_2, h_2) → G_1
  85. Intersect(g_2, h_2) → H_1
  86. Intersect(h_2, l) → I_1
  87. Intersect(g_2, m) → J_1
  88. Intersect(f_2, q) → K_1
  89. Intersect(h_2, r) → L_1
  90. Polygon(C, G_1, A) → poly1, a_2, c_2, g_3
  91. Circle(A, c_2) → d_2
  92. Segment(A, E_1) → i_2
  93. Intersect(d_2, i_2, 1) → M_1
  94. Segment(A, M_1) → n_2
  95. Point(n_2) → N_1
  96. Vector(A, N_1) → u_2
  97. Translate(C, u_2) → C'
  98. Translate(G_1, u_2) → O_1
  99. Translate(A, u_2) → A'_1
  100. Polygon(C', O_1, A'_1) → poly1', a'_1, c', o_1
  101. Polygon(C, H_1, B) → poly2, b_2, c_3, h_3
  102. Circle(B, c_2) → e_2
  103. Segment(B, F_1) → p_2
  104. Intersect(e_2, p_2, 1) → P_1
  105. Segment(B, P_1) → q_2
  106. Point(q_2) → Q_1
  107. Vector(B, Q_1) → v_2
  108. Translate(C, v_2) → C'_1
  109. Translate(H_1, v_2) → R_1
  110. Translate(B, v_2) → B'_1
  111. Polygon(C'_1, R_1, B'_1) → poly2', b'_1, c'_1, r_2
  112. Polygon(C, A_1, J_1, H_1) → poly3, c_4, a_3, j_3, h_4
  113. Segment(H_1, F_1) → s_2
  114. Point(s_2) → S_1
  115. Vector(H_1, S_1) → w_2
  116. Translate(รูปหลายเหลี่ยม3, t_2) → รูปหลายเหลี่ยม3'
  117. Translate(C, w_2) → C'_2
  118. Translate(A_1, w_2) → T_1
  119. Translate(J_1, w_2) → U_1
  120. Translate(H_1, w_2) → V_1
  121. Polygon(C'_2, T_1, U_1, V_1) → poly3', c'_2, t_3, u_3, v_3
  122. Polygon(B_1, J_1, H_1, I_1) → poly4, b_3, j_4, h_5, i_3
  123. Segment(H_1, E_1) → f_3
  124. Point(f_3) → W_1
  125. Vector(H_1, W_1) → w_3
  126. Translate(B_1, w_3) → Z_1
  127. Translate(J_1, w_3) → A_2
  128. Translate(H_1, w_3) → B_2
  129. Translate(I_1, w_3) → C_2
  130. Polygon(Z_1, A_2, B_2, C_2) → poly4', z_1, a_4, b_4, c_5
  131. Polygon(I_1, H_1, B) → poly5, b_5, i_4, h_6
  132. Segment(B, Z_1) → k_3
  133. Point(k_3) → D_2
  134. Vector(B, D_2) → d_3
  135. Translate(I_1, d_3) → E_2
  136. Translate(H_1, d_3) → F_2
  137. Translate(B, d_3) → B'_2
  138. Polygon(E_2, F_2, B'_2) → poly5', b'_2, e_3, f_4
  139. Polygon(C, L_1, C_1) → poly6, c_6, c_7, l_4
  140. Segment(C_1, C') → m_3
  141. Point(m_3) → G_2
  142. Vector(C_1, G_2) → n_3
  143. Translate(C, n_3) → C'_3
  144. Translate(L_1, n_3) → H_2
  145. Translate(C_1, n_3) → I_2
  146. Polygon(C'_3, H_2, I_2) → poly6', i_5, c'_3, h_7
  147. Intersect(h_2, f_2) → J_2
  148. Polygon(L_1, D_1, A, J_2) → poly7, l_5, d_4, a_5, j_5
  149. Segment(D_1, N_1) → p_3
  150. Point(p_3) → K_2
  151. Vector(D_1, K_2) → q_3
  152. Translate(L_1, q_3) → L_2
  153. Translate(D_1, q_3) → M_2
  154. Translate(A, q_3) → A'_2
  155. Translate(J_2, q_3) → N_2
  156. Polygon(L_2, M_2, A'_2, N_2) → poly7', l_6, m_4, a'_2, n_4
  157. Polygon(B, A, 4) → poly8, r_3, s_3, g_4, k_4, O_2, P_2
  158. Polygon(A, B, C) → poly9, c_8, a_6, b_6